时间扩展取样集合卡尔曼滤波同化模拟探空试验研究

目前,集合卡尔曼滤波同化预报循环系统主要的计算量和时间都花费在样本成员的预报上,小样本数虽能减少计算量,但样本数过少,特别是当有模式误差时,又会导致滤波发散。为了提高集合卡尔曼滤波同化预报循环系统的效率并减轻滤波发散等问题,开展了基于WRF的时间扩展取样集合卡尔曼滤波同化模拟探空的试验研究,以考察其在中尺度模式中的同化效果。预报时对一组样本数为Nb的样本,不仅在分析时刻取样,同时也在分析时刻前和后每间隔Δt时间进行M次取样,即在没增加预报样本数的情况下,增加了分析样本成员数(Nb+2M×Nb),从而在保证不降低分析精度的前提下,也达到减小集合卡尔曼滤波的计算量的要求。通过一系列试验来检验时间扩展取样的时间间隔Δt及在分析时刻前和后最大取样次数M对同化结果的影响。试验结果表明,当选择合适的Δt和M时,时间扩展集合卡尔曼滤波的同化效果非常接近于样本数为(1+2M)×Nb的传统集合卡尔曼滤波效果,具有一定的可行性。     

Time-Expanded Sampling Approach for Ensemble Kalman Filter:Experiment Assimilation of Simulated Soundings

In the Ensemble Kalman Filter (EnKF) data assimilation-prediction system, most of the computationtime is spent on the prediction runs of ensemble members. A limited or small ensemble size does reduce thecomputational cost, but an excessively small ensemble size usually leads to filter divergence, especially whenthere are model errors. In order to improve the efficiency of the EnKF data assimilation-prediction systemand prevent it against filter divergence, a time-expanded sampling approach for EnKF based on the WRF(Weather Research and Forecasting) model is used to assimilate simulated sounding data. The approachsamples a series of perturbed state vectors from Nb member prediction runs not only at the analysis time(as the conventional approach does) but also at equally separated time levels (time interval is △t) beforeand after the analysis time with M times. All the above sampled state vectors are used to construct theensemble and compute the background covariance for the analysis, so the ensemble size is increased fromNb to Nb+2M￡Nb=(1+2M)×Nb) without increasing the number of prediction runs (it is still Nb). Thisreduces the computational cost. A series of experiments are conducted to investigate the impact of △t (thetime interval of time-expanded sampling) and M (the maximum sampling times) on the analysis. The resultsshow that if △t and M are properly selected, the time-expanded sampling approach achieves the similareffect to that from the conventional approach with an ensemble size of (1+2M)×Nb, but the number ofprediction runs is greatly reduced.     

基于集合卡尔曼滤波的土壤温湿度同化试验

以通用陆面模式CLM 3.0(Community Land Model 3.0)为模型算子,基于集合卡尔曼滤波(Ensemble Kalman Filter,En KF)发展了一个土壤温湿度同化系统,主要用于改进模式对土壤温湿度和地表水热通量的模拟精度,并考察集合样本数、同化频率及不同观测量的组合对同化效果的影响。该系统同化了FLUXNET两个站点(阿柔和Bondville)不同土壤深度、不同时间频率的土壤温度和湿度数据。通过对阿柔站不同集合样本数的设计,综合考虑计算成本和计算精度,最终将集合样本数设置为40。通过分析三种同化方案对同化频率的敏感性得出,同化土壤温度最为敏感,同时同化土壤温湿度次之,同化土壤湿度最不敏感。对于阿柔站点,同化系统对不同土壤深度温度和湿度的模拟精度均能提高90%,潜热通量的均方根误差由94.0 W·m~(-2)降为46.3 W·m~(-2),感热通量均方根误差由55.9 W·m~(-2)降为24.6 W·m~(-2)。Bondville站点浅层土壤温度的改进在30%左右,深层土壤温度改进达到60%,对土壤湿度的改进均在70%以上,潜热通量和感热通量的均方根误差分别从57.4 W·m~(-2)和54.4 W·m~(-2)降为51.0 W·m~(-2)和42.5 W·m~(-2)。试验结果表明,同化站点土壤温湿度数据对土壤水热状况及通量的模拟改进非常有效,同时也验证了同化土壤水分遥感产品的可行性和必要性。     

集合Kalman滤波同化理论及其数值试验

集合Kalman滤波用于数值试验有着坚实的理论基础.本文介绍了集合Kalman滤波理论及其技术实现, 在此基础上搭建了集合Kalman滤波同化系统, 用MM5模式同化了实测探空资料并作了48 h的预报试验, 并将预报结果与实测值及4D VAR同化的结果作了比较.试验结果表明: 集合Kalman滤波同化探空资料可以改进MM5模式的预报效果, 且集合Kalman滤波同化后模式的预报效果明显优于4D VAR同化后模式的预报效果.     

集合卡尔曼滤波同化多普勒雷达资料的数值试验

利用集合卡尔曼滤波(EnKF)在云数值模式中同化模拟多普勒雷达资料,并考察了不同条件下EnKF同化方法的性能.结果显示,经过几个同化周期后,EnKF分析结果非常接近真值.单多普勒雷达资料EnKF同化对雷达位置不太敏感,双雷达资料同化结果在同化的初期阶段比单雷达资料同化结果准确.同化由反射率导出的雨水比直接同化反射率资料更有效,联合同化径向速度和雨水有利于提高同化分析效果.协方差对EnKF同化效果起着非常重要的作用,考虑模式全部预报变量与径向速度协方差的同化效果比仅考虑速度场与径向速度协方差的同化效果好.雷达资料缺值降低了同化效果,此时增加地面常规观测资料的同化可以明显提高同化分析效果.EnKF同化技术对雷达观测资料误差不太敏感.初始集合对同化分析有较大影响.EnKF同化受集合大小和观测资料影响半径.同化对模式误差较敏感.利用EnKF同化双多普勒雷达资料,分析了一次梅雨锋暴雨过程的中尺度结构.结果表明,EnKF同化技术能够从双多普勒雷达资料反演暴雨中尺度系统的动力场、热力场和微物理场,反演的风场是较准确的,反演的热力场和微物理场分布也是基本合理的.中低层切变线是此次暴雨的主要动力特征,对流云表现为低层辐合、高层辐散并有垂直上升运动伴随,其热力特征表现为低层是低压区,高层为高压区,中部为暖区而上、下部为冷区,水汽、云水和雨水分别集中在对流云体内、上升气流区和强回波区.     

集合Kalman滤波资料同化技术及研究现状

针对国内集合Kalman滤波资料同化领域的研究空白,对该技术的背景、理论、优势以及存在的问题做了简要描述,对目前国际上的主要研究成果做了介绍,并给出了该方法可能的发展方向。     

集合卡尔曼滤波同化探空资料的数值试验

应用集合卡尔曼滤波（Ensemble Kalman Filter;EnKF）方法,同化了2005年7月一次暴雨过程的探空观测资料,并用非静力中尺度模式MM5进行数值模拟试验。结果表明：在理想模式的假设下,即假设真实模拟和所产生的集合用的是同一个模式并有相同的初始误差,EnKF方法同化的分析结果较好。如果不运用EnKF方法同化探空观测资料,则集合预报结果和不加扰动的单个数值预报结果都没有EnKF方法同化过的好。     

Coupling Ensemble Kalman Filter with Four-dimensional Variational Data Assimilation

This study examines the performance of coupling the deterministic four-dimensional variational assimilation system (4DVAR) with an ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme (E4DVAR) benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence: the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.     

多物理ETKF在暴雨集合预报中的初步应用

基于集合转换卡尔曼滤波（ETKF）的初值扰动方法是目前集合预报领域热点方法之一,但应用在短期集合预报中仍存在离散度不够、误差较大等问题。考虑到在区域短期集合预报中,模式不确定性和边界不确定性的影响不能忽略,本文尝试在ETKF生成分析扰动的过程中,同时考虑初值不确定性、物理不确定性与边界不确定性,进而构建多初值、多物理、多边界ETKF集合,并以2010年9月30日到10月8日海南岛特大暴雨作为研究个例,对其在暴雨集合预报中的应用展开初步研究,重点分析多种物理参数化过程对预报结果的影响。结果表明,多物理过程的ETKF（多物理ETKF）和单物理过程的ETKF（单一ETKF）均优于对照预报,多物理ETKF优势更加明显,其均方根误差、离散度等指标均得到很好的改善;对于降水采用SAL方法进行检验,发现多物理ETKF对于降水位置的预报有明显的改善,对于特大暴雨的强度预报也略有改善。研究表明,在ETKF初值扰动中加入多种物理过程,可以有效改善短期集合的离散度,提高预报准确率,有良好的发展前景和应用潜力。     

基于集合Kalman滤波数据同化的热带气旋路径集合预报研究

构建了一个基于集合Kalman滤波数据同化的热带气旋集合预报系统,通过积云参数化方案和边界层参数化方案的9个不同组合,采用MM5模式进行了不同时间的短时预报。对预报结果使用“镜像法”得到18个初始成员,为同化提供初始背景集合。将人造台风作为观测场,同化后的结果作为集合预报的初值,通过不同参数组合的MM5模式进行集合预报。对2003～2004年16个台风个例的分析表明,初始成员产生方法能够对热带气旋的要素场、中心强度和位置进行合理扰动。同化结果使台风强度得到加强,结构更接近实际。基于同化的集合路径预报结果要优于未同化的集合预报。使用“镜像法”增加集合成员提高了预报准确度,路径预报误差在48小时和72小时分别低于200 km和250 km。     

集合卡尔曼平滑和集合卡尔曼滤波在污染源反演中的应用

此文目的是讨论污染源反演问题的统计方法.基于Bayes估计理论,该文将资料同化中的集合平滑、集合卡尔曼平滑和集合卡尔曼滤波应用在污染源反演问题中.在详细给出污染源反演的集合平滑、集合卡尔曼平滑和集合卡尔曼滤波的严格数学表达后,用一个简单的模型演示了集合卡尔曼平滑和集合卡尔曼滤波在污染源反演中的可行性,并且通过对比理想试验结果比较了集合卡尔曼平滑和集合卡尔曼滤波方法在反演污染源排放的效果,讨论了观测误差和污染源先验误差估计对反演结果的影响.试验结果表明在观测间隔小和观测误差小的情况下,集合卡尔曼滤波和集合卡尔曼平滑都可以有效地反演出随时间变化的污染源排放.当观测误差增大时,集合卡尔曼滤波和集合卡尔曼平滑的反演效果都有一定降低,但是反演误差的增加少于观测误差的增加,同时集合卡尔曼平滑(Ensemble Kalman smoother,简称EnKS)对观测误差比集合卡尔曼滤波(Ensemble Kalman filter,简称EnKF)更为敏感.当观测时间间隔较大时,EnKF不能对没有观测时的污染源排放进行估计,仅能对有观测时的污染源排放进行较好的反演.而EnKS可以利用观测对观测时刻前的污染源排放进行反演,因此其效果明显好于EnKF,并且在观测时间间隔较大的情况下依然可以较好地反演出污染源排放.试验结果还显示污染源排放的先验误差估计对反演的结果有较大影响.     

集合卡尔曼滤波数据同化在一维波动方程中的应用

简要回顾了集合卡尔曼滤波(EnKF：Ensemble Kalman Filter)数据同化方法的发展历史,并介绍了EnKF数据同化方法的基本原理,利用一维非线性波动方程进行了数值试验。EnKF数据同化方法的实现过程简单可行。避免了EKF中协方差演变方程预报过程中出现的计算不准确和关于协方差矩阵的大量数据的存储问题,最主要的是EnKF可以有效控制模式变量估计误差方差的增长,改善预报效果。     

A Multivariate Empirical Orthogonal Function-Based Scheme for the Balanced Initial Ensemble Generation of an Ensemble Kalman Filter

The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.     

集合卡尔曼滤波同化多普勒雷达资料的观测系统模拟试验

本文将集合卡尔曼滤波同化技术应用到对流尺度系统中,实施了基于WRF模式的同化单部多普勒雷达径向风和反射率因子的观测系统模拟试验,验证了其在对流尺度中应用的可行性和有效性,并对同化系统的特性进行了探讨。试验表明:WRF-EnKF雷达资料同化系统能较准确分析模式风暴的流场、热力场、微物理量场的细致特征;几乎所有变量的预报和分析误差经过同化循环后都能显著下降,同化分析基本上能使预报场在各层上都有所改进,对预报场误差较大层次的更正更为显著;约8个同化循环后,EnKF能在雷达反射率、径向风观测与背景场间建立较可靠的相关关系,使模式各变量场能被准确分析更新,背景场误差协方差在水平方向和垂直方向都有着复杂的结构,是高度非均匀、各项异性和流依赖的;集合平均分析场做的确定性预报在短时间内能较好保持真值场风暴的细节结构,但预报误差增长较快。     

Assimilating the LAI Data to the VEGAS Model Using the Local Ensemble Transform Kalman Filter: An Observing System Simulation Experiment

Information on the spatial and temporal pat- terns of surface carbon flux is crucial to understanding of source/sink mechanisms and projection of future atmospheric CO2 concentrations and climate. This study presents the construction and implementation of a terrestrial carbon cycle data assimilation system based on a dynamic vegetation and terrestrial carbon model Vegetation-Global-Atmosphere-Soil （VEGAS） with an advanced assimilation algorithm, the local ensemble transform Kalman filter （LETKF, hereafter LETKF-VEGAS）. An observing system simulation experiment （OSSE） framework was designed to evaluate the reliability of this system, and numerical experiments conducted by the OSSE using leaf area index （LAI） observations suggest that the LETKF -VEGAS can improve the estimations of leaf carbon pool and LAI significantly, with reduced root mean square errors and increased correlation coefficients with true values, as compared to a control run without assimilation. Furthermore, the LETKF-VEGAS has the potential to provide more accurate estimations of the net primary productivity （NPP） and carbon flux to atmosphere （CFta）.     

基于集合卡尔曼滤波的土壤水分同化试验

集合卡尔曼滤波是由大气数据同化发展的新的顺序同化算法,它利用蒙特卡罗方法计算背景场的误差协方差矩阵,克服了卡尔曼滤波需要线性化的模型算子和观测算子的难点。我们发展了一个基于集合卡尔曼滤波和简单生物圈模型(SiB2,Simple Biosphere Model)的单点陆面数据同化方案。利用1998年7月6日至8月9日青藏高原GAME-Tibet实验区MS3608站点的观测数据进行了同化试验。结果表明,利用集合卡尔曼滤波的数据同化方法可以明显地提高表层、根区、深层土壤水分的估算精度。     

Ideal Case Study of Adaptive Localization in Storm-scale Ensemble Kalman Filter Assimilation

This study explores the use of the hierarchical ensemble filter to determine the localized influence of ob-servations in the Weather Research and Forecasting ensemble square root filtering (WRF-EnSRF) assimilation system. With error correlations between observations and background field state variables considered, the adaptive localization approach is applied to conduct a series of ideal storm-scale data assimilation experiments using simulated Doppler radar data. Comparisons between adaptive and empirical localization methods are made, and the feasibility of adaptive locali-zation for storm-scale ensemble Kalman filter assimilation is demonstrated. Unlike empirical localization, which relies on prior knowledge of distance between observations and background field, the hierarchical ensemble filter provides con-tinuously updating localization influence weights adaptively. The adaptive scheme improves assimilation quality during rapid storm development and enhances assimilation of reflectivity observations. The characteristics of both the observation type and the storm development stage should be considered when identifying the most appropriate localization method. Ultimately, combining empirical and adaptive methods can optimize assimilation quality.     

Assimilation of Hourly Surface Observations with the Canadian High-Resolution Ensemble Kalman Filter

An hourly-cycling ensemble Kalman filter (EnKF) working at 2.5?km horizontal grid spacing is implemented over southern Ontario (Canada) to assimilate Meteorological Terminal Aviation Routine Weather Reports (METARs) in addition to the observations assimilated operationally at the Canadian Meteorological Centre. This high-resolution EnKF (HREnKF) system employs ensemble land analyses and perturbed roughness length to prevent an ensemble spread that is too small near the surface. The HREnKF then performs continuously for a four-day period, from which twelve-hour ensemble forecasts are launched every six hours. The impact on analyses and short-term forecasts of assimilating METAR data is given special attention.

It is shown that using ensemble land surface analyses increases near-surface ensemble spreads for temperature and specific humidity. Perturbing roughness length enlarges the spread for surface wind. Given sufficient ensemble spread, the four-day case study shows that the near-surface model state is brought closer to surface observations during the cycling process. The impact of assimilating surface data can also be seen at higher levels by using aircraft reports for verification. The ensemble forecast verification suggests that METAR data assimilation improves ensemble forecasts of air temperature and dewpoint near the surface up to a lead time of six hours or even longer. However, only minor improvement is found in surface wind forecasts.     

集合KALMAN滤波和最优插值方法在不同观测分布的比较理想试验

目前一种比较流行并且可行的同化方法-集合Kalman滤波(EnKF)能够计算依赖于流的误差统计量。理论上,EnKF能够比最优插值、三维变分等更准确地计算误差统计量,能更好地融合背景场和观测场的信息。作者利用二维平流扩散方程经过10天的同化循环,比较不同观测分布的情况下EnKF和最优插值(OI)的模拟能力。理想试验结果显示,随着观测分布密度的减小,尤其是当观测的分辨率大于OI估计的相关尺度时,集合Kalman滤波的结果比最优插值有更明显的改进。     

过去状态估计之集合Kalman滤波扩充状态变量法研究

集合Kalman滤波是由大气数据同化发展的新的同化算法,它利用蒙特卡罗方法计算背景场的误差协方差矩阵,克服了Kalman滤波需要线性化的模型算子和观测算子的难点。但是这种同化方法是一种顺序数据同化方法,无法对过去状态变量进行同化订正。而过去状态的估计对于建立大气或海洋历史资料库、获得准确的数值预报初始场有着重要的意义。本文在集合Kalman滤波同化方法的基础上,提出了可以对过去状态进行估计的集合Kalman滤波扩充状态变量法,然后分别采用空气质量方程和Lorenz系统对这种方法进行了检验。数值试验结果表明,这种方法可以对非线性系统中的过去状态变量进行有效的估计订正,说明该方法是可行的。